Salby M.L. Fundamentals of Atmospheric Physics

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1 A Global View

Brightness Temperature

(a) 1200 March 4, 1984

-30

-60

-90 0

60 120 180 240 300 360

(b) Time-Mean

330 T(K) 190

-30

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-90 0 60 120 180 240 300

360

300 T(K) 210

Figure 1.25 Global cloud image constructed from 11-/zm radiances measured aboard six satel-

lites simultaneously viewing the earth. (a) Instantaneous cloud field at 1200 GMT on March 4,

1984. (b) Time-mean cloud field for January-March 1984. Gray scale displays equivalent black-

body temperature as indicated.

1.3 Radiative Equilibrium of the Planet

Time-mean cloudiness also reveals the North Atlantic and North Pacific

storm tracks, where convection is organized by synoptic weather systems. Sev-

eral such systems are evident in the instantaneous cloud field in Fig. 1.25a.

In the Southern Hemisphere, they are distributed throughout a nearly con-

tinuous storm track. This feature of the tropospheric circulation reflects the

relative absence of major orographic features in the Southern Hemisphere,

which, by exciting planetary waves, disrupt the zonal circulation of the North-

ern Hemisphere.

Clouds are also important in chemical processes. Condensation and precip-

itation constitute the primary removal mechanism for many chemical species.

Gaseous pollutants that are water soluble are absorbed in cloud droplets and

eliminated when those droplets precipitate to the surface. Referred to as rain

out, this mechanism also scavenges aerosol pollutants, which serve as conden-

sation nuclei for cloud droplets and ice crystals. Although they improve air

quality, these scavenging mechanisms transfer pollutants to the surface, where

they can produce "acid rain."

Another chemical process in which clouds figure importantly relates to

the ozone hole in Fig. 1.19b. Because moisture is sharply confined to the

troposphere, clouds form in the stratosphere only under exceptionally cold

conditions. The Antarctic stratosphere is one of the coldest sites in the atmo-

sphere and, as a result, is populated by a rare cloud form. Thin and very high,

polar stratospheric clouds (PSCs) are common over the Antarctic. Heteroge-

neous chlorine chemistry that takes place on the surfaces of cloud particles

is responsible for the formation of the ozone hole each year during Austral

spring.

1.3 Radiative Equilibrium of the Planet

The driving force for the atmosphere is the absorption of solar energy at the

earth's surface. Over timescales long compared to those controlling the redis-

tribution of energy, the earth-atmosphere system is in thermal equilibrium, so

the net energy gained must vanish. Consequently, absorption of solar radia-

tion, which is concentrated in the visible and termed shortwave (SW) radiation,

must be balanced by emission to space from the planet's surface and atmo-

sphere of terrestrial radiation, which is concentrated in the IR and termed

longwave (LW) radiation. This basic principle leads to a simple estimate of the

mean temperature of the planet.

The earth intercepts a beam of SW radiation of cross-sectional

area 7ra 2

and

flux Fs, as illustrated in Fig. 1.26. A fraction of the intercepted radiation, the

albedo d, is reflected back to space by the planet's surface and components

of the atmosphere. The remainder of the incident SW flux: (1 - d)F~, is then

absorbed by the earth-atmosphere system and distributed across the globe as

it spins in the line of the beam.

Radiation

0.5

~TT)

Radiation

{A.

Brn)

Figure

1.26

Schematic

radiation intercepted

the earth and LW radiation emitted by it.

1.4 The Global Energy Budget

To maintain thermal equilibrium, the earth and atmosphere must re-emit

to space LW radiation at exactly the same rate. Also referred to as

outgoing

longwave radiation

(OLR), the emission to space of terrestrial radiation is

described by the Stefan-Boltzmann law

7rB = o.T 4, (1.29)

where 7rB represents the energy flux integrated over wavelength that is emit-

ted by a blackbody at temperature T and where or is the Stefan-Boltzmann

constant. Integrating the emitted LW flux over the surface of the earth and

equating the result to the SW energy absorbed by the earth-atmosphere sys-

tem results in the simple energy balance

(1 - d)F s

"Ira 2 --

4"n'a 2 o-T 4 ,

(1.30.1)

where

T e

is the equivalent blackbody temperature of the earth. Then

4o- (1.30.2)

provides a simple estimate of the planet's temperature. An incident SW flux of

F s = 1372 W

m -2

and an albedo of d -- 0.30 lead to an equivalent blackbody

temperature for earth of

= 255 K. This value is some 30 K colder than the

global-mean surface temperature, T~ = 288 K.

The discrepancy between Ts and Te follows from the different ways the

atmosphere processes SW and LW radiation. Although nearly transparent to

SW radiation (wavelengths A ~ 0.5 /xm), the atmosphere is almost opaque

to LW radiation (A ~ 10/zm) that is re-emitted by the planet's surface. For

this reason, SW radiation passes freely to the earth's surface, where it can

be absorbed, but LW radiation emitted by the planet's surface is captured by

the overlying air. Energy absorbed in an atmospheric layer is re-emitted, half

upward and half back downward. The upwelling radiation is absorbed again in

overlying layers, which subsequently re-emit that energy in similar fashion. This

process is repeated until LW energy is eventually radiated beyond all absorbing

components of the atmosphere and rejected to space. By inhibiting the transfer

of energy from the earth's surface, repeated absorption and emission by the

atmosphere traps LW energy and elevates the surface temperature over what

it would be in the absence of an atmosphere.

The elevation of surface temperature that results from the atmosphere's

different transmission characteristics to SW and LW radiation is known as

the

greenhouse effect.

The greenhouse effect is controlled by the IR opac-

ity of atmospheric constituents, which radiatively insulate the planet. In the

earth's atmosphere, the primary absorbers are water vapor, clouds, and car-

bon dioxide. Ozone, methane, and nitrous oxide are also radiatively active at

wavelengths of terrestrial radiation, as are aerosols and CFCs.

44 1 A Global View

1.4 The Global Energy Budget

Because it follows from a simple energy balance, the equivalent blackbody tem-

perature provides some insight into where LW radiation is ultimately emitted

to space. The value

T e

= 255 K corresponds to the middle troposphere, above

most of the water vapor and where clouds are abundant. Most of the energy

received by the atmosphere is supplied from the earth's surface, where SW

radiation is absorbed. Transfers of energy from the surface constitute a heat

source for the atmosphere, whereas IR cooling to space in the middle tro-

posphere constitutes a heat sink for the atmosphere. These energy transfers

drive the atmosphere and make its circulation behave as a global heat engine

in the energy budget of the earth.

Energy absorbed at the earth's surface must be transmitted to the middle

troposphere, where it is rejected to space. From the time it is absorbed at

the surface as SW radiation until it is eventually rejected to space, energy

assumes a variety of forms. Most of the energy transfer between the earth's

surface and the atmosphere occurs through LW radiation. In addition, energy

is transferred through thermal conduction, which is referred to as the transfer

sensible heat,

and through the transfer of

latent heat,

when water vapor

absorbed by the atmosphere condenses and precipitates back to the surface.

In addition, energy is stored internally in the atmosphere in both ther-

mal and mechanical forms. The thermal or internal energy of air, which is

measured by temperature, represents the random motion of molecules. Me-

chanical energy is represented in the distribution of atmospheric mass within

the earth's gravitational field (potential energy) and in the motion of air (ki-

netic energy). These internal forms of energy are involved in the redistribution

of energy within the atmosphere, but they do not contribute to globally inte-

grated transfers between the Earth's surface, the atmosphere, and deep space.

1.4.1 Global-Mean Energy Balance

The globally averaged energy budget is illustrated in Fig. 1.27. Incoming solar

energy is distributed across the earth. Therefore, the global-mean SW flux

incident on the top of the atmosphere is given by/~ -

Fs/4 -

343 W m -2,

where the factor 4 represents the ratio of the surface area of the earth to

the cross-sectional area of the intercepted beam of SW radiation (Fig. 1.26).

Of the incident 343 W m -2, a total of 106 W m -2 (approximately 30%) is

reflected back to space: 21 W m -2 by air, 69 W m -2 by clouds, and 16 W m -2

by the surface. The remaining 237 W m -2 is absorbed in the earth-atmosphere

system. Of this, 68 W m -2 (about 20% of the incident SW flux) is absorbed by

the atmosphere: 48 W m -2 by atmospheric water vapor, ozone, and aerosol

and 20 W m -2 by clouds. This leaves 169 W m -2 to be absorbed by the

surfacemnearly 50% of that incident on the top of the atmosphere.

1.4

The Global Energy Budget

Incident

Shortwave Flux

343

.....................

Atmo

~, Back-

\\~ Scattered

Reflected

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Reflectec

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Absorbed

by HzO, 03,

Aerosol

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Reflected Outgoing

Shortwave Flux Longwave Flux

21 69 16 22 90 125

.................... ; ................ I ............................

Emitted Emitted

s by

Hzi, COz,

Aerosol Surface-

Atmosphere

Emitted ~ Heat Transfer

by Surface

========.'_:=======8=====

................. o/.

Reflected

~/]/Sur face

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:iii!i!~4~iiiii

:::::::::::::::::::

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by Clouds iby

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/ t

/ ~ Emitted Sensible Latent

/ ~ by HzO, COz, Heat Heat

Aerosol~Clouds Fllux FllUX

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Figure 1.27 Global-mean energy budget

(W m-Z).

Updated from

Understanding Climate

Change

(1975) with recent satellite measurements of the earth's radiation budget.

Additional

sources."

Ramanathan (1987), Ramanathan

al.

(1989).

The 169 W m -2 absorbed at the ground must be re-emitted to maintain

thermal equilibrium of the earth's surface. At a global-mean surface temper-

ature of Ts - 288 K, the surface emits 390 W m -2 of LW radiation according

to (1.29)~far more than it absorbs as SW radiation. Excess LW emission must

be balanced by transfers of energy from other sources. Owing to the green-

house effect, the surface also receives LW radiation that is emitted downward

by the atmosphere in the amount 327 W m -2. Collectively, these contributions

result in a net transfer of radiative energy to the surface:

SW absorption + LW absorption - LW emission = Net radiative forcing

from atmosphere of surface

169 W m -2 -k- 327 W m -2 - 390 W m -2 - +106 W m -2

The surplus of 106 W m -2 represents net "radiative heating of the surface."

For equilibrium, this must be balanced by transfers of sensible and latent heat

to the atmosphere. Sensible heat transfer accounts for 16 W m -2 through con-

duction with the atmosphere. Latent heat transfer accounts for the remaining

90 W m -z, which follows from evaporative cooling of the oceans. Were it not

for these supplemental forms of energy transfer, the earth's surface would

have to be some 50 K warmer to balance the net absorption of radiant energy.

The energy budget of the atmosphere must also balance to zero to maintain

thermal equilibrium. The atmosphere receives 68 W m -2 directly through

absorption of SW radiation. Of the 390 W m -2 of LW radiation emitted by

the earth's surface, only 22 W m -2 passes freely through the atmosphere and

1 A Global

View

is rejected to space. The remaining 368 W m -2 is absorbed by the atmosphere:

120 W m -2 by clouds and 248 W m -2 by water vapor, CO2, and aerosol. The

atmosphere loses 327 W m -2 through LW emission to the earth's surface.

Another 215 W m -2 is rejected to space: 90 W m -2 emitted by clouds and 125

W m -2 emitted by water vapor, CO2, and other minor constituents. Collecting

these contributions gives the net flux of radiative energy to the atmosphere:

SW absorption + LW absorption - LW emission - LW emission = Net radiative forcing

from surface to surface to space of atmosphere

68Wm -2 + 368Wm -2 - 327Wm -2 - 215Wm -2 = -106Wm -2.

The deficit of 106 W m -2 represents net "radiative cooling of the atmosphere,"

cooling that is balanced by the transfers of sensible and latent heat from the

earth's surface.

1.4.2 Horizontal Distribution of Radiative Transfer

The preceding discussion focuses on vertical transfers associated with the

global-mean energy balance. Were the absorption of SW energy and the emis-

sion of LW energy uniform across the earth, those vertical transfers could

accomplish most of the energy exchange needed to preserve thermal equi-

librium. However, geometrical considerations, variations in optical properties,

and cloud cover make radiant energy transfer nonuniform across the globe.

Even if optical properties of the earth-atmosphere system were homoge-

neous, the absorption of solar energy would not be distributed uniformly.

At low latitudes, SW radiation arrives nearly perpendicular to the earth (see

Fig. 1.26). A pencil of radiation incident on the top of the atmosphere is dis-

tributed there across a perpendicular cross section. Consequently, the flux of

energy crossing the top of the atmosphere at low latitudes equals that passing

through the pencil. On the other hand, SW radiation at high latitudes arrives

at an oblique angle. A pencil of radiation incident on the top of the atmo-

sphere is distributed there across an oblique cross section. Because the latter

has an area greater than that of a perpendicular cross section, the flux of en-

ergy crossing the top of the atmosphere is less than that passing through the

pencil and therefore less than that arriving at low latitudes.

The daily-averaged SW flux incident on the top of the atmosphere is re-

ferred to as the

insolation.

Insolation depends on the

solar zenith angle,

which

is measured from local vertical, and on the length of day. Figure 1.28 shows

the insolation as a function of latitude and season. During equinox, insolation

is a maximum on the equator and decreases poleward like the cosine of lati-

tude. At solstice, the maximum insolation occurs over the summer pole, with

values uniformly high across much of the summer hemisphere. In the win-

1.4 The Global Energy Budget

90*

80*

70*

60 ~

50*

40*

30"

20 ~

tl.I

I0 ~

0 o

I'-

-I00

...!

-200

-500

-40 ~

_50 ~

-60"

-70*

-80*

-90 ~

JAN

,.-,,,,

JAN

FEB MAR APRIL MAY JUNE JULY AUG SEPT OCT NOV DEC

i 0

__10__. 0

-')ti/

i '

[ /l/l/ /

I / / ,///_

ii/ '/W,

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/hJl)l l l

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I I

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e,I." I

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....

/ t

#wo, i J

~:.-.-:::k:.':

--~

"i,

L':'_:_'::

FEB MAR APRIL MAY JUNE JULY AUG SEPT OCT NOV DEC

MONTH

Figure 1.28 Average daily

SW flux

incident on the top of the atmosphere (cal

cm-2day-1),

as a function of latitude and time of year. After List

(1958).

ter hemisphere, insolation decreases sharply with latitude and vanishes at the

polar-night terminator,

beyond which the earth is not illuminated. 5

Optical properties of the atmosphere also lead to nonuniform heating of

the planet. At low latitudes, SW radiation passes almost vertically through

the atmosphere, so the distance traversed through absorbing constituents is

minimized. However, at middle and high latitudes, SW radiation traverses

the atmosphere along a slant path that involves a much longer distance and

therefore results in greater absorption. A similar effect is brought about by

scattering of SW radiation by atmospheric aerosol, which increases sharply

5The

slight asymmetry between the hemispheres evident in

Fig. 1.28

follows from the eccen-

tricity of the earth's orbit, which brings the planet closest to the sun during January and farthest

from the sun during

July.

48 1 A Global

View

with solar zenith angle, Each of these atmospheric optical effects leads to

more SW energy reaching the earth's surface at low latitudes than at high

latitudes.

Optical properties of the earth's surface introduce similar effects. These

emerge in OLR and reflected SW radiation observed by the Earth Radiation

Budget Experiment (ERBE), which are shown in Fig. 1.29 during northern

winter. Figure 1.29a shows the distribution of albedo. Low latitudes, which

account for much of the earth's surface area, have extensive coverage by ocean.

(a) ALBEDO

(b) LONGWAVE (Wm "2)

Figure 1.29 Top-of-the-atmosphere radiative properties for December-February derived

from the Earth Radiation Budget Experiment (ERBE), which was on board the ERBS and

NOAA-9 satellites: (a) albedo, (b) outgoing longwave radiation, (c) net radiation. Adapted from

Hartmann (1993).

(continues)

1.4 The Global

Energy Budget 49

Figure 1.29

(Continued)

Those regions are characterized by very low albedo and thus absorb most of

the SW energy incident on them. High latitudes, particularly in the winter

hemisphere, have extensive coverage by snow and ice. Having a high albedo,

those surfaces reflect back to space much of the SW energy incident on them,

especially at large solar zenith angles, which increases scattering. Cloud cover

adds to the high albedo of extratropical regions, for example, in the storm

tracks. A high albedo is also evident in the tropics, where deep convection leads

to maxima over the Amazon Basin, tropical Africa, and Indonesia. Flanking

these regions are areas of low albedo that correspond to cloud-free oceanic

regions in the subtropics and between tropical landmasses.

Outgoing longwave radiation (Fig. 1.29b) is dominated by the poleward

decrease of temperature, which results in OLR decreasing steadily with lat-

itude (1.29). At middle and high latitudes, anomalously low OLR is found

over the Tibetan Plateau and Rocky Mountains, where cold surface temper-

atures reduce LW emission. Anomalously low OLR is also found near the

equator, over the convective centers of South America, Africa, and Indone-

sia. High cloud tops in those regions have very low temperatures, so their LW

emissions are substantially smaller than those from the surface in neighboring

cloud-free regions. In fact, subtropical latitudes are marked by distinct max-

ima of OLR in regions flanking organized convection. Sinking motion there,

which compensates rising motion inside the ITCZ, inhibits cloud formation

and precipitation, maintaining arid zones that typify the subtropics.

The

net radiation, which is defined as the difference between the SW radia-

tion absorbed and the LW radiation emitted by the earth-atmosphere system,

is shown in Fig. 1.29c. Although the global-mean net radiation must vanish

for thermal equilibrium (1.30), this need not be the case locally. Low latitudes

are characterized by a surplus of net radiation (warming), whereas high lat-